The solution of the differential equation `(x^2+1)(dy)/(dx)+(y^2+1)=0` is a. `y=2+x^2` b. `y=(1+x)/(1-x)` c. `y=x(x-1)` d. `y=(1-x)/(1+x)`

Explanation

To solve the differential equation \((x^2 + 1) \frac{dy}{dx} + (y^2 + 1) = 0\), we will follow these steps:

### Step 1: Rearranging the Equation
We start by rearranging the given differential equation to separate the variables:
\[ (x^2 + 1) \frac{dy}{dx} = - (y^2 + 1) \]
Now, we can separate the variables:
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